To alleviate this problem, it has been proposed to apply deep learning methods [1]}, [2]}, [3]}, [4]} and Convolutional Neural Networks (CNNs) in 3D voxelized grids. This has been used to accelerate the search for solutions of the discrete Poisson equation [5]}, to directly regress the fluid velocity fields given an implicit surface description [6]}, or to compute fluid simulations velocities from a set of reduced parameters [7]}. However, the underlying 3D CNN architectures working with spatial voxels tend to feature large memory footprints and computationally demanding inference. To work around this problem, it has been proposed to replace the GPs with Geodesic Convolutional Neural Networks (GCNNs) [8]}, [9]} to emulate a simulator [10]}, [11]}. Given a set of generic surfaces parametrized as meshes, a GCNN is trained to predict their aerodynamic characteristics, as computed by standard CFD packages [12]}, [13]}, [14]}. These characteristics are then used to write an objective function that is differentiable with respect to the shape parameters. To maximize performance, the objective function is minimized with respect to these parameters. This makes it possible to deal with more complex parameterization but fails to estimate uncertainties, which hampers the use of so-called exploration-and-exploitation algorithms such as those discussed below, which are very powerful for these kinds of applications [15]}.
